When using a bump or displacement node and bump only or displacement and bump in the material settings, the shade smooth option seems to not be working. Instead the geometry starts to show, auto smooth does not help either. Adding more geometry fixes the issue but defeats the purpose of using a bump map in the first place. This issue makes it unusable in many scenarios. Any ideas on how to fix this are highly appreciated!

When using a bump or displacement node and bump only or displacement and bump in the material settings, the shade smooth option seems to not be working. Instead the geometry starts to show, auto smooth does not help either. Adding more geometry fixes the issue but defeats the purpose of using a bump map in the first place. This issue makes it unusable in many scenarios. Any ideas on how to fix this are highly appreciated!

Edit: .blend file added.